function Z = pp_unsigned(A, B)
    len_a = length(A);
    len_b = length(B);
    Z = zeros(len_b, len_a+len_b-1);
    for i = 1:len_a,
        Z(len_a-i+1,:) = [zeros(1,i-1) A(i)*B zeros(1,len_a-i)];
    end
end